Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 703 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 11 days (d) 22 days
2. 2.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 12 days (d) 19 days
3. 3.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 11 days (d) 6 days
4. 4.If 6 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹96 (b) ₹504 (c) ₹73 (d) ₹84
5. 5.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹351 (c) ₹312 (d) ₹39
6. 6.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 1 day (d) 7 days
7. 7.If 6 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹720 (b) ₹130 (c) ₹66 (d) ₹120
8. 8.If 9 pens cost ₹27, how much do 6 pens cost? (a) ₹162 (b) ₹24 (c) ₹18 (d) ₹21
9. 9.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 14 days (d) 4 days
10. 10.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 5 days
11. 11.If 2 pens cost ₹50, how much do 6 pens cost? (a) ₹300 (b) ₹175 (c) ₹54 (d) ₹150
12. 12.₹234 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹117 (b) ₹234 (c) ₹26 (d) ₹208
13. 13.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 13 days (d) 5 days
14. 14.If 9 notebooks cost ₹144, how much do 4 notebooks cost? (a) ₹139 (b) ₹576 (c) ₹80 (d) ₹64
15. 15.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 7 days (d) 17 days
16. 16.If 4 kites cost ₹48, how much do 5 kites cost? (a) ₹60 (b) ₹49 (c) ₹72 (d) ₹240
17. 17.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹120 (d) ₹75
18. 18.If 2 kites cost ₹38, how much do 5 kites cost? (a) ₹95 (b) ₹114 (c) ₹190 (d) ₹41
19. 19.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 5 days (d) 6 days
20. 20.If 4 pens cost ₹100, how much do 7 pens cost? (a) ₹200 (b) ₹700 (c) ₹103 (d) ₹175
21. 21.If 7 kites cost ₹140, how much do 6 kites cost? (a) ₹840 (b) ₹139 (c) ₹140 (d) ₹120
22. 22.If 5 kites cost ₹30, how much do 4 kites cost? (a) ₹30 (b) ₹29 (c) ₹120 (d) ₹24
23. 23.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹180 (c) ₹20 (d) ₹160
24. 24.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 2 days (d) 11 days
25. 25.If 8 kites cost ₹160, how much do 3 kites cost? (a) ₹60 (b) ₹155 (c) ₹80 (d) ₹480
26. 26.If 6 kites cost ₹114, how much do 10 kites cost? (a) ₹118 (b) ₹1140 (c) ₹209 (d) ₹190
27. 27.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹28 (d) ₹42
28. 28.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 25 days
29. 29.If 9 kites cost ₹81, how much do 3 kites cost? (a) ₹27 (b) ₹36 (c) ₹243 (d) ₹75
30. 30.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 15 days (d) 9 days
31. 31.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹156 (b) ₹182 (c) ₹91 (d) ₹26
32. 32.If 7 notebooks cost ₹28, how much do 8 notebooks cost? (a) ₹29 (b) ₹32 (c) ₹36 (d) ₹224
33. 33.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹38 (c) ₹39 (d) ₹19
34. 34.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹245 (d) ₹175
35. 35.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 14 days (d) 9 days
36. 36.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹56 (d) ₹42
37. 37.If 2 kites cost ₹30, how much do 7 kites cost? (a) ₹105 (b) ₹35 (c) ₹120 (d) ₹210
38. 38.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 4 days
39. 39.If 2 notebooks cost ₹44, how much do 4 notebooks cost? (a) ₹46 (b) ₹110 (c) ₹176 (d) ₹88
40. 40.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹126 (d) ₹140

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